3^(2x) = 75 Solve the equation accurate to three decimal places

Problem: 3^(2x)=75 is an exponential equation.
  To simplify, we need to apply logarithm property: log(x^y) = y*log(x)
 to bring down the exponent that is in terms of x.
 Taking "log" on both sides:
log(3^(2x))=log(75 )
(2x)log(3)=log(75)
Divide both sides by log(3) to isolate "2x ":
(2x * log (3)) /(log(3))= (log(75))/(log(3))
2x=(log(75))/(log(3))
Multiply both sides by 1/2 to isolate x:
(1/2)*2x=(log(75))/(log(3))*(1/2)
Note: You will get the same result when you divide both sides by 2.
The equation becomes:
x=(log(75))/(2log(3))
x~~1.965    Rounded off to three decimal places
 
To check, plug-in x=1.965 in 3^(2x)=75 :
3^(2*1.965)=?75
3^(3.93)=?75
75.0043637 ~~75  TRUE
 
Conclusion: x~~1.965 is the final answer.